1 . (1)求导函数
.
(2)求定积分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01974d041922cb667e503a94dc1acac3.png)
(2)求定积分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7655033ea2c7bfa0c9de1f348741a292.png)
您最近一年使用:0次
2021-09-02更新
|
256次组卷
|
2卷引用:江西省上饶市横峰中学2020-2021学年高二下学期期中考试数学(理)试题
2 . 我们要计算由抛物线
、
轴以及直线
所围成的曲边区域的面积
,可用
轴上的分点0、
、
、…、
、1将区间
分成
个小区间,从第二个小区间起,在每一个小区间上作一个小矩形,使得每个矩形的左上端点都在抛物线
上,这么矩形的高分别为
、
、…、
,矩形的底边长都是
,设所有这些矩形面积的总和为
,就有
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/58a58585-2072-4fd8-aa69-9740f5b39d6a.png?resizew=200)
(1)求
的表达式,并求出面积
;(可以利用公式
)
(2)利用上述方法,探求由函数
、
轴、
轴以及直线
和所围成的区域的面积
.(可以利用公式:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6a2eba56d4f2d1670b0256b8d86b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c350e626893ba12c028b6c8bc4ea8d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc7040ad5dd0ebafac0e9f23bd54812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b176553f857ff6e6641d79c9e83be10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7d1d8923879a6fdaf839d87aafeff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf343294853aef9035ed93efb09ec2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6a2eba56d4f2d1670b0256b8d86b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a12c3439a5339dd2ae4c91e52466f3c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/58a58585-2072-4fd8-aa69-9740f5b39d6a.png?resizew=200)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ee4f17114ccb24847c7228ae17ba8c.png)
(2)利用上述方法,探求由函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2eff609c6043c2a89a6dd163fe2244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e28ccf6acba4afeb5983cc1bc575d13b.png)
您最近一年使用:0次
3 . 已知平方和公式:
,其中
.
(1)记
,其中
,求
的值;
(2)已知
,求自然数
的值;
(3)抛物线
.
轴及直线
围成了如图(1)的阴影部分,
与
轴交于点
,把线段
分成
等份,作以
为底的内接矩形如图(2),阴影部分的面积为
,
等于这些内接矩形面积之和.
,当
时的极限值.
![](https://img.xkw.com/dksih/QBM/2020/8/6/2522228892000256/2522958075985920/STEM/57322956baba4cdebe449f79eeb00cfd.png?resizew=610)
图(3)中的曲线为开口向右的抛物线
,抛物线
.
轴及直线
围成了图中的阴影部分,请利用极限平方和公式.反函数或割补法等知识求出阴影部分的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c698639cdba709641d3c91ea1798abfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb5d8ebd8544c7c90f5772eb7185498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1edd770d288fa52a742d73ef9d5edae7.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3735968325345a8f5a23bbb2723354a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cf1ba54a1d09dcd2fd68add8a107bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9057a085e325652e874898b69aa0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89846a5f66a8f9259a0b07cae9776084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc3ec69887a76bfb07531b5d5745255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d154b00d2363a51a93657d941f07ff.png)
![](https://img.xkw.com/dksih/QBM/2020/8/6/2522228892000256/2522958075985920/STEM/57322956baba4cdebe449f79eeb00cfd.png?resizew=610)
图(3)中的曲线为开口向右的抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff51fab7db7694fab8b42aa4f1bf295.png)
您最近一年使用:0次
2019高一下·全国·专题练习
4 . 利用定积分的定义,计算
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e33848413000803ccc9687474dce27.png)
您最近一年使用:0次
2019高二下·全国·专题练习
名校
5 . 计算下列定积分:
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9622371ce1ba479752f981e851d0afbb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52c0ecbde416e5278a14b46d7e9c321.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28edcb8a5b98eefa0d91b10a1190f1a7.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52bd6612d57c21c14a51f5276257acde.png)
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6 . 已知函数f(x)=
求f(x)在区间[-1,3π]上的定积分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ca757a1be2589eacc1faa90e21dac0.png)
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2018-02-25更新
|
527次组卷
|
2卷引用:高中数学人教A版选修2-2 第一章 导数及其应用 1.5 定积分的概念
7 . (1)求函数
的导数;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8fe3eedd655e22aa824d4e99aadebc1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0206f8827097efb62fc11c3cd045a436.png)
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